91Ó°ÊÓ

Compute the inverse matrix, if it exists, using elementary row operations (as shown in Example 3 ). $$\left(\begin{array}{rrr} 1 & 0 & -2 \\ -3 & -1 & 6 \\ 2 & 1 & -5 \end{array}\right)$$

Find all solutions \((x, y)\) of the given systems, where \(x\) and \(y\) are real numbers. $$\left\\{\begin{array}{l}y=\log _{2}(x+1) \\\y=5-\log _{2}(x-3)\end{array}\right.$$

Graph the systems of inequalities. $$\left\\{\begin{array}{l} x \geq 0 \\ y \geq 0 \\ y<\sqrt{x} \\ x \leq 4 \end{array}\right.$$

Use matrices to solve each system of equations. $$\left\\{\begin{aligned} x+2 y-z-2 w &=5 \\ 2 x+y+2 z+w &=-7 \\ -2 x-y-3 z-2 w &=10 \\ z+w &=-3 \end{aligned}\right.$$

Find all solutions \((x, y)\) of the given systems, where \(x\) and \(y\) are real numbers. $$\left\\{\begin{array}{l}2^{x} \cdot 3^{y}=4 \\\x+y=5\end{array}\right.$$

Find all solutions of each system. $$\left\\{\begin{aligned} 2 x-\quad y+ \quad z &=4 \\ x+3 y+2 z &=-1 \\ 7 x \quad\quad +5 z=11 \end{aligned}\right.$$

Graph the systems of inequalities. $$\left\\{\begin{array}{l} x \geq 0 \\ y \geq 0 \\ y \leq 1-x^{2} \end{array}\right.$$

Use the addition-subtraction method to find all solutions of each system of equations. $$\left\\{\begin{array}{l} 5 x+6 y=4 \\ 2 x-3 y=-3 \end{array}\right.$$

Evaluate the determinants. \(\left|\begin{array}{rrr}3 & 0 & 0 \\ 0 & 19 & 0 \\ 0 & 0 & 10\end{array}\right|\)

Compute the inverse matrix, if it exists, using elementary row operations (as shown in Example 3 ). $$\left(\begin{array}{rrr} 1 & 2 & -1 \\ 0 & 3 & 0 \\ -4 & 0 & 5 \end{array}\right)$$